Question

Daca x=3√2-5√8 si y=-$2^{-1}$-0,5 atunci:
a)(x+y)²=?
b)$(\frac{x}{2}+ \frac{y}{2} )(x-y)$

Answer 1

x = 3√2 - 5√8 = 3√2 - 5√2³ = 3√2 - 5·2√2 = 3√2 - 10√2
x = - 7√2
y =- 2^ - 1 · 0, 5 = - 1/2 · 5/10 = -  5/20 = - 1/4
y = - 1/4
a) ( x + y)² = ( - 7√2 - 1/4)² = ( - 7√2)² + 2· ( - 7√2) · ( - 1/4) + ( - 1 /4)² =
                 = 49·2 + 2·7 √2 /4 + 1/16
                 = 98 + 14√2/4 + 1/16
                 = 98 + 7√2/2 +1/16
b)( x/2 + y /2)(x - y) = ( - 7√2 /2 - 1/4 : 2)( - 7√2 + 1/4)
                             = ( - 7√2 /5 - 1/2)( - 7√2 + 1/4)